The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation. The fundamental solution is obtained in the form of the projection operator defining the subspace of solutions to the Dirac equation. It is illustrated by the analysis of the ground state and the spin precession of the Dirac electron in the field of two counterpropagating plane waves with left and right circular polarizations. Interrelations between the fundamental solution and approximate partial solutions is discussed and a criterion for evaluating the accuracy of approximate solutions is suggested.

We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to familiar photonic networks where driven two-level atoms exchange photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D $XX$ spin chains representing spin waveguides. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization-group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.

We study the dynamics of quantum coherence under Unruh thermal noise and seek under which condition the coherence can be frozen in a relativistic setting. We find that the frozen condition is either (i) the initial state is prepared as an incoherence state or (ii) the detectors have no interaction with the external field. That is to say, the decoherence of the detectors' quantum state is irreversible under the influence of thermal noise induced by Unruh radiation. It is shown that quantum coherence approaches zero only in the limit of an infinite acceleration, while quantum entanglement could reduce to zero for a finite acceleration. It is also demonstrated that the robustness of quantum coherence is better than entanglement under the influence of the atom-field interaction for an extremely large acceleration. Therefore, quantum coherence is more robust than entanglement in an accelerating system and the coherence-type quantum resources are more accessible for relativistic quantum information processing tasks.

Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement “quantum simulators.” Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. The fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.

We present a three-cavity network model with two modes in each cavity and a nonlinear medium that generates a Kerr-type interaction via both self-phase and cross-phase modulation processes. We have two main goals. The first one is to generate a multipartite maximally entangled state (MES), starting from the ground state of the system. We address the problem both without and with dissipation. Second, we want to protect the MES from decoherence. While studying the MES, we analyze different bipartite and multipartite entanglement measures. We also study the effect of an avoided level crossing identified by the critical behavior of the entanglement measures, thus showing that the quantum correlations act as a witness for such phenomena. Our findings provide the quantum tools to perform the operation of generation and protection of a maximally entangled state in a cavity QED environment.

Quantum memories for optical and microwave photons provide key functionalities in quantum processing and communications. Here we propose a protocol well adapted to solid-state ensemble-based memories coupled to cavities. It is called Stark echo modulation memory (SEMM) and allows large storage bandwidths and low noise. This is achieved in an echo-like sequence combined with phase shifts induced by small electric fields through the linear Stark effect. We investigated the protocol for rare-earth nuclear spins and found a high suppression of unwanted collective emissions that is compatible with single-photon-level operation. Broadband storage together with high fidelity for the Stark retrieval process is also demonstrated. SEMM could be used to store optical or microwave photons in ions and/or spins. This includes nitrogen-vacancy centers in diamond and rare-earth-doped crystals, which are among the most promising solid-state quantum memories.

Direct state tomography (DST) using weak measurements has received wide attention. Based on the concept of coupling-deformed pointer observables presented by Zhang et al. [Y.-X. Zhang, S. Wu, and Z.-B. Chen, Phys. Rev. A 93, 032128 (2016)], a modified direct state tomography (MDST) is proposed, examined, and compared with other typical state tomography schemes. MDST has exact validity for measurements of any strength. We identify the strength needed to attain the highest efficiency level of MDST by using statistical theory. MDST is much more efficient than DST in the sense that far fewer samples are needed to reach DST's level of reconstruction accuracy. Moreover, MDST has no inherent bias when compared to DST.

The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^L$ polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities—the polarizabilities ${\alpha }_L$, the electric-to-magnetic cross susceptibilities ${\alpha }_{\mathrm{E}L\to \mathrm{M}(L\mp 1)}$, and the electric-to-toroidal-magnetic cross susceptibilities ${\alpha }_{\mathrm{E}L\to \mathrm{T}L}$—are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions $F_2$ with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities—the electric nuclear shielding constants ${\sigma }_{\mathrm{E}L\to \mathrm{E}L}$, the near-nucleus electric-to-magnetic cross susceptibilities ${\sigma }_{\mathrm{E}L\to \mathrm{M}(L\mp 1)}$, and the near-nucleus electric-to-toroidal-magnetic cross susceptibilities ${\sigma }_{\mathrm{E}L\to \mathrm{T}L}$—involve one or two terminating $F_2\left(1\right)$ series and for each $L$ may be rewritten in terms of elementary functions. Numerical values of the far-field dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the fine-structure constant $\alpha$ on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in $\alpha Z$, where $Z$ is the nuclear charge number, are also derived for all types of the far-field and near-nucleus susceptibilities considered in the paper.

The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field is determined from the Ehrenfest-like equations of motion. These equations for the average values of the translational and spin degrees of freedom are derived from the Schrödinger-Pauli wave equation, and they form a set of nine coupled nonlinear evolution equations. The numerical and analytic solutions of these equations are obtained for the combination of the rotating magnetic field of a wave carrying orbital angular momentum and a static magnetic field. The running wave traps the atom only in the transverse direction, while the standing wave traps the atom also in the direction of the beam.

The photoelectron momentum shifts along the laser propagation are investigated by the time-dependent perturbation theory for diatomic molecules, such as ${\mathrm{H}}_2{}^{+}, {\mathrm{N}}_2$, and ${\mathrm{O}}_2$. Such longitudinal momentum shifts characterize the photon momentum sharing in atoms and molecules, and oscillate with respect to photon energies, presenting the double-slit interference structure. The atomic and molecular contributions are disentangled analytically, which gives an intuitive picture of how the double-slit interference structure is formed. Calculation results show that the longitudinal photoelectron momentum distribution depends on the internuclear distance, molecular orientation, and photon energy. The current laser technology is ready to verify these theoretical predictions.

The ac Stark shift, or light shift, is a physical phenomenon that plays a fundamental role in many applications ranging from basic atomic physics to applied quantum electronics. Here, we discuss experiments testing light-shift theory in a cold-atom cesium fountain clock for the Cs $D_2$ transition (i.e., $6{}^2{S}_{1/2}\to 6{}^2{P}_{3/2}$ at 852 nm). Cold-atom fountains represent a nearly ideal system for the study of light shifts: (1) The atoms can be perturbed by a field of arbitrary character (e.g., coherent field or nonclassical field); (2) there are no trapping fields to complicate data interpretation; (3) the probed atoms are essentially motionless in their center-of-mass reference frame, $T$ ∼ 1 μK; and (4) the atoms are in an essentially collisionless environment. Moreover, in the present work the resolution of the Cs excited-state hyperfine splittings implies that the $D_2$ ac Stark shift contains a nonzero tensor polarizability contribution, which does not appear in vapor phase experiments due to Doppler broadening. Here, we test the linearity of the ac Stark shift with field intensity, and measure the light shift as a function of field frequency, generating a “light-shift curve.” We have improved on the previous best test of theory by a factor of 2, and after subtracting the theoretical scalar light shift from the experimental light-shift curves, we have isolated and tested the tensor light shift for an alkali $D_2$ transition.

We simulate the dissipative evolution of a vortex in a trapped finite-temperature dilute-gas Bose-Einstein condensate using first-principles open-systems theory. Simulations of the complete stochastic projected Gross-Pitaevskii equation for a partially condensed Bose gas containing a single quantum vortex show that the transfer of condensate energy to the incoherent thermal component without population transfer provides an important channel for vortex decay. For the lower temperatures considered, this effect is significantly larger that the population transfer process underpinning the standard theory of vortex decay, and is the dominant determinant of the vortex lifetime. A comparison with the Zaremba-Nikuni-Griffin kinetic (two-fluid) theory further elucidates the role of the particle transfer interaction, and suggests the need for experimental testing of reservoir interaction theory. The dominance of this particular energetic decay mechanism for this open quantum system should be testable with current experimental setups, and its observation would have broad implications for the dynamics of atomic matter waves and experimental studies of dissipative phenomena.

Taking an open quantum system approach, we derive a collective equation of motion for the dynamics of a matter-wave bright soliton moving through a thermal cloud of a distinct atomic species. The reservoir interaction involves energy transfer without particle transfer between the soliton and thermal cloud, thus damping the soliton motion without altering its stability against collapse. We derive a Langevin equation for the soliton center-of-mass velocity in the form of an Ornstein-Uhlenbeck process with analytical drift and diffusion coefficients. This collective motion is confirmed by simulations of the full stochastic projected Gross-Pitaevskii equation for the matter-wave field. The system offers a pathway for experimentally observing the elusive energy-damping reservoir interaction and a clear realization of collective Brownian motion for a mesoscopic superfluid droplet.

The protocol for counterfactual transmission of a qubit [Z.-H. Li et al., Phys. Rev. A 92, 052315 (2015)] relies on the counterfactuality of transmissions of bit 1 and of bit 0. Since counterfactuality of transmission of bit 0 is not established, the claim of counterfactuality of transmission of a quantum state is not established too.

We address criticisms made in the preceding Comment by Vaidman regarding our claims of counterfactuality of transmission of a quantum state in our recent work.

This study reinterprets an earlier experimental photoelectron kinetic energy spectrum of the negative ion of lanthanum [A. M. Covington, D. Calabrese, J. S. Thompson, and T. J. Kvale, J. Phys. B 31, L855 (1998)] by carrying out relativistic configuration interaction (RCI) photodetachment calculations. The results confirm the earlier RCI calculation for the electron affinity of lanthanum (0.545 eV) [S. M. O'Malley and D. R. Beck, Phys. Rev. A 79, 012511 (2009)] and revise it to a slightly larger value of 0.550 eV, thus modifying the experimental interpretation of $0.47\pm 0.02$ eV. The calculation also yields the binding energies of the other thirteen bound states of ${\mathrm{La}}^{-}$. Good agreement has been found when these energies are compared to the results of a recent experimental study on ${\mathrm{La}}^{-}$ [C. W. Walter, N. D. Gibson, D. J. Matyas, C. T. Crocker, K. A. Dungan, B. R. Matola, and J. Rohlén, Phys. Rev. Lett. 113, 063001 (2014)]. Finally, our analysis confirms the transition energy for the potential laser cooling transition of ${}^3{F}_2^e\to {}^3{D}_1^o$ in ${\mathrm{La}}^{-}$.

Below- and near-threshold harmonic generation provides a potential approach to achieve a high conversion efficiency of vacuum-ultraviolet and extreme-ultraviolet sources for the advancement of spectroscopy. Here, we perform a time-dependent density functional theory study for the nonperturbative treatment of below- and near-threshold harmonic generation of CO and ${\mathrm{N}}_2$ diatomic molecules subject to short near-infrared laser pulses and aligned parallel to the laser field polarization. We find that with the use of different driving laser pulse shapes, we can control and enhance harmonic generation through the excited-state resonance structures. Depending on the pulse shape, the enhancement can reach five to seven orders of magnitude as compared to the reference sine-squared laser pulse of the same duration. The results for different driving laser intensities are also presented and discussed in detail.

In this paper, the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method is derived for the case of $N$ identical bosons with internal degrees of freedom. The theory for bosons with internal degrees of freedom constitutes a generalization of the MCTDHB method that substantially enriches the many-body physics that can be described. We demonstrate that the numerically exact solution of the time-dependent many-body Schrödinger equation for interacting bosonic particles with internal degrees of freedom is now feasible. We report on the MCTDHB equations of motion for bosons with internal degrees of freedom and their implementation for a general many-body Hamiltonian with one-body and two-body terms, both of which may depend on the internal states of the considered particles and time. To demonstrate the capabilities of the theory and its software implementation integrated in the mctdh-x software, we apply MCTDHB to the emergence of fragmentation of parabolically trapped bosons with two internal states: we study the ground state of $N=100$ bosons as a function of the separation between the state-dependent minima of the two parabolic potentials. To quantify the coherence of the system, we compute its normalized first-order correlation function. We find that the coherence within each internal state of the atoms is maintained, while it is lost between the different internal states. This is a hallmark of a kind of fragmentation absent in bosons without internal structure. We term the emergent phenomenon “composite fragmentation.”

We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore, the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [F. E. Becerra et al., Nat. Photon. 7, 147 (2013)] can achieve this aim with an appropriately chosen encoding strategy.